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Reasoning and decision
Reasoning and decision:
human or machine?
How can a typically human activity such as reasoning be performed by machines? To answer this question we have to understand how our minds
function. This is determined not only by physical reality, but also by our
beliefs, goals and preferences.
>>> Andreas Herzig, CNRS senior scientist
at the Institut de recherche en informatique
de Toulouse (IRIT, joint UPS/CNRS/UT1/UT2/
INPT lab)
We don’t know everything, our beliefs may be
erroneous and we live in a world that changes
all the time. Despite all these difficulties we
are able to reason and to make decisions quite
successfully. Our abilities to learn and to revise
our beliefs are crucial for this.
We not only reason about nature and physical
reality, but also about the other human
agents in our environment and with social
reality as created by man: society and its
institutions, such as norms and conventions,
things that are allowed and things that are
forbidden, contracts, etc. Indeed, language and
communication may be considered to be the
first of these institutions: in dialogue we exploit
the fact that others know the conventions of
communication, allowing them to interpret
what we say. An example of a convention is to
avoid contradictions and to stay focused on the
subject.
Anthropomorphism
Theories of possibility and
logics of modality
The overall aim is to implement artificial agents
in computers. How can one relate concept
analysis and computer programs? For several
years now, the researchers working on the
“Reasoning and Decision” theme at IRIT have
adopted a classical research avenue, viz. formal
approaches, allowing for rigorous and verifiable
proofs. Their main tools are possibility theory
and modal logics, and the procedure is to start
by formal modeling (including concept analysis).
This is then followed by an investigation of the
mathematical properties and the development
of automatic or semi-automatic reasoning
procedures.
Contact : [email protected]
IRIT: Institut de recherche en informatique de Toulouse/
Toulouse Insitute of Computer Science Research
What we have said up to now applies to human
agents, and one might wonder what all this
has to do with computer science. However,
it appears that the central concepts in our
discourse apply to artificial agents too. Such an
anthropomorphic point of view was adopted in
Artificial Intelligence right from its beginnings
in the 60s and in multi-agent systems in the 80s.
Of course, how agents reason and decide is
not only investigated in computer science,
but originally in the humanities and in social
sciences, viz. in psychology, philosophy,
linguistics, cognitive science, and economy.
It is therefore a multidisciplinary object of
study, and the researchers of IRIT very often
collaborate with linguists and psychologists of
the Toulouse labs “Cognition, Langues, Langage,
Ergonomie” (CLLE, université Toulouse 2) and
the economists of the “Toulouse School of
Economics” (TSE, université Toulouse 1).
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>>> Rodin’s The Thinker at Saint Dié.
© Christian Amet/Creative Commons
Paul Sabatier University — Scientific Magazine — issue n°11
Reasoning and
decision
Language and
representing knowledge
Reading a text, analyzing and summarizing it: these processes are not unique
to humans anymore according to new work by researchers at the IRIT laboratory who are studying the automatic treatment of language
>>> Nathalie Aussenac-Gilles,
CNRS senior scientist, and Laure Vieu, CNRS
scientist, researchers at the IRIT (UPS/CNRS/
INP/UT1/UT2)
“ You feel confused?
You don’t have a boyfriend?
No social life? No dreams?
You want to be more like
sitcom actors? Then go for
this TV show and watch it
over and over again! ”
>>> Caption:
In opinion mining of short texts, such as
forum comments, the main goal is to find
out if the author has a favorable opinion of
the discussed topic. The example illustrates
the limitations of algorithms based only
on word spotting. The advice given in the
article indicates
a positive opinion of
the show. However, taking into account
the whole context and with sufficient
background knowledge, it can be seen that
“ no social life ” characterizes an audience
for which the author has no respect, so that
recommending the show for that particular
audience actually leads to a negative
opinion about the show itself.
Among the first challenges faced by the Artificial
Intelligence (AI) program was to reproduce the very
human ability of producing and understanding
linguistic messages. This is all the more difficult as
such activity is thought of being a mark of human
intelligence. Natural language processing makes
linguistic analyses accessible to computer systems,
from the handling of synonyms (lexical level), for
instance, to the identification of verb complements
(syntaxic level), finding what a pronoun refers to
(semantic level) or the relation between two sentences
(discourse level). This, in turn, is used for information
extraction, machine translation, or automated
summary production. Collaboration between linguists
and computer scientists has proved very useful in this
respect, and researchers in the NLP at IRIT have
a long standing partnership with linguistic groups
at Université Toulouse II (CLLE-ERSS and J
acques Lordat Lab).
Information explosion
The path followed since the inception of the AI
program has been tremendously transformed by the
explosion of the amount of data available in natural
language (whether written or oral) either published on
the web or produced by companies or users. Managing
this abundance opens up new avenues for testing
hypotheses on languages, and the development of
efficient tools for analysis. It also favours sharing of
information, knowledge discovery and corroboration.
A major objective in the domain is to give some
structure to the areas of knowledge that need to be
formalized, by finding connections between relevant
entities, their properties and the concepts they involve.
This usually goes under the name of ontology. In the
medical domain, many ontologies have been designed,
often starting from thesaurii, such as MESH or
UMLS, or from automated analyses of medical texts to
jump-start the formalization process. These ontologies
provide richer definitions of medical concepts, of
relations between pathologies, treatments and
anatomic aspects, etc. They are used to characterize
the information available in patient files, good
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practice guidelines or scientific papers, for verification
and corroboration, and more globally to fuel decision
processes with recent research results.
Opinion mining
The main activity of our team contributes to the
formalization of different elements that take part in
the semantics of a text. Our work is concerned with
the globality of a text or a discourse, how lexical and
syntaxic elements combine but also how relations
within and between sentences, paragraphs and other
textual elements contribute to the construction of
meaning. Research on ontologies includes these results
to organize knowledge and build systems that can help
to identify and extract information from texts. This
also implies the development of tools to help model
and maintain ontologies.
The end result combines knowledge and its linguistic
expression. It is put to the test by a range of
applications, mainly opinion mining (to understand
such phenomena as corporate or private e-reputations,
or product reviews), dialog analysis, text mining
and automated ontology building. Our research
also involves industrial partnerships (eg ACTIA
Automotive, Synapse Development), institutional
funding via ANR grants, for instance, for computer
aided diagnostic of electronic failure, or geographical
database integration.
Contact : [email protected], [email protected],
[email protected]
Reasoning and
decision
Probability Theory
alone cannot handle
all facets of uncertainty
People constantly deal with pieces of information that are incomplete, uncertain,
inaccurate, and sometimes inconsistent. To face this issue, scientists naturally
resort to probability theory. But this approach does not take into account where
uncertainty comes from.
Probability theory as a tool for representing uncertainty
has long existed, but it often does away with the fact that
there may be several reasons for being uncertain. The main
reason evoked is the variability of natural phenomena and
of data coming from repeated measurements. Hence the
frequentist’s view of probabilities that is often taken for
granted.
>>> Didier Dubois and Henri Prade,
CNRS senior scientists at the Institut
de Recherche en Informatique de Toulouse
(IRIT, UPS/CNRS/UT1/ UT2/INPT
>>> Results for risk calculation application
page 6
Thought lotteries
Another very common reason for uncertainty is the
plain lack of information, which alone may prevent
agents from knowing whether statements of interest are
true or false. This kind of “poor” information often takes
the form of an incomplete set of propositions in classical
logic, or appears as an interval of possible numerical
values of an ill-known quantity, or even as a set of
attributes that does not allow for the precise description
of an object. To understand such situations, we need
another probabilistic concept, so-called subjectivistism,
where a probability does not reflect an ideal frequency,
but represents, in a betting framework, the price of a
thought lottery that yields an euro if the concerned
event occurs. This concept claims that it makes sense
to represent any incomplete information situation by
means of a unique probability distribution. But this
view can be challenged: such a representation is not
scale-invariant, and does not depend on the origin of
uncertainty. It is more natural to represent incomplete
information by means of a mere set of possible values,
often called the “epistemic state” ” in Artificial
Intelligence.
Uncertainty theories
It makes sense to be able to tell variability and
incompleteness apart in the scope of information
processing. Several new theories try to address this
issue, such as possibility theory, evidence theory and
imprecise probability theory. In such settings, instead of
representing any information state by means of a unique
probability distribution, sets thereof, or even random
sets, are used. The confidence attached to an event
occuring is then quantified by a probability interval,
measuring certainty by its lower bound and plausibility
by its upper bound. Sometimes such quantification
is difficult to justify. All that can be said in some
cases is that some events are more likely than others.
One is then led to use qualitative representations of
uncertainty, that turn out to be instrumental in dealing
with exception-tolerant reasoning.
Possibilistic Logic
When information is incomplete, the human
mind resorts to reasoning patterns that enable
useful conclusions to be tentatively drawn despite
incompleteness. Such conclusions can be questioned
upon the arrival of new pieces of information. In this
case, reasoning becomes non-monotonic and presupposes
the truth of anything that is considered normal in the
current informational context. This form of reasoning
is not amenable to classical logic. It requires logic with
embedded priorities, such as possibilistic logic. Such
logic is also instrumental in the problem of merging
partially inconsistent pieces of information.
For more than 20 years, our team has been working
on the construction of formal frameworks that are wide
enough to enrich the expressive power of traditional
approaches to uncertainty, both probabilistic and
logic-based. For the last 10 years or so we have
cooperated with public research laboratories in the area
of environmental risk analysis, such as BRGM or IRSN.
In risk analysis, the usual methodology is first to build
a mathematical model of some potentially hazardous
phenomenon. Then in a second step, we must check on
the basis of data collected on-site in an area of concern,
whether the probability of a risky event is above some
acceptable, say, pollution, threshold. But the collected
objective data are often incomplete and part of the
information must come from expert opinion. We have
developed risk analysis methods based on imprecise
probabilities encoded as possibility distributions, so as to
separately handle uncertainty due to known variability
and uncertainty due to lack of data.
Contacts : [email protected],
[email protected]
Paul Sabatier University — Scientific Magazine — issue n°11
Reasoning and
decision
Game theory, emotion and trust:
from social sciences to artificial
intelligence
In recent times, game theory has begun to take into account both motivations
and more and more complex emotions such as trust, guilt or shame. These are
useful concepts for designing robots similar to humans.
>>>Dominique LONGIN and Emiliano LORINI,
CNRS senior scientists
at the IRIT (UPS/CNRS/UT1/UT2/INP).
During the last century, game theory became the
dominant paradigm in social sciences for modeling and
for explaining social interaction between human agents
and economic agents (states, companies, banks, etc.).
The goal of this theory is to explain and predict social
actors’ choices in strategic interaction contexts, that is,
when the choice of a given agent depends on what other
agents decide to do. Classical game theory is based on
a very simple conceptual frame including the concepts
of preference and action. But following the work of the
economists John Charles Harsanyi and Robert Aumann,
game theory began to include the concepts of knowledge
and belief in order to model strategic interaction
situations with incomplete information. More recently,
the concepts of emotion and trust have become central
to this theory. Empirical evidence and psychological
theories show that emotions such as guilt, shame or
regret affect human strategic decisions. Furthermore,
it has been proved that trust plays a crucial role not
only in individual decision making but also in social
interaction by fostering cooperation.
Reasoning from emotions
In recent years, game theory has become the most used
theoretical framework in the area of multi-agent systems
(MAS). MAS are a part of artificial intelligence (AI),
whose goal is to develop interaction models between
artificial autonomous agents (for instance, models of
cooperation and coordination, negotiation models, etc.).
Similarly, emotion and trust have become central themes
in the area of AI. Computational models of autonomous
cognitive agents capable of reasoning by taking into
account human users’ emotions, and whose decisions
are influenced by their own emotions, already exist.
Several models of trust have been proposed in the area
of MAS: statistical and socio-cognitive models of trust
and reputation models. These models provide formal and
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>>> “Les tricheurs” (Caravaggio, Kimbell Art Museum)
abstract specifications that can be used for developing
several applications such as web services, reputation
systems (EBay for instance), semantic web, embodied
conversational agents and cognitive robotics.
Facial expressions
Work at the LILaC group at IRIT aims to develop logical
models of social interaction based on game theory and
on psychological theories of emotion and of trust. These
models can be exploited as a base for implementing
artificial agents capable of reasoning from concepts of
emotion and trust during interaction with a human
user or with other agents and whose strategic decisions
are influenced by their emotions. For instance, a logical
model of emotions based on counterfactual reasoning,
such as regret or guilt, has been developed. This model
has been recently used in the ANR project CECIL for
expressing such emotions in a multimodal fashion (for
example, facial and vocal expressions, and gestures).
Contacts : [email protected],
[email protected]
Reasoning and
decision
My computer
knows me so well
How much can computers learn to know us ? Machine learning is a research
area where considerable progress has been made in the last 30 years.
Computers are now able to recognize their users’ voice
or handwriting. Computers have learnt to discriminate
human features. Can a menu recommender system, for
example, learn what its user likes in order to suggest
dishes to her liking? As we can see, “knowing” the user
in this case means knowing her culinary preferences.
>>> Jérôme MENGIN,
UPS assistant professor,
researcher at IRIT (UPS/CNRS/INP/UT1/UT2)
Decision-making support
More generally, knowing the user’s preferences must
help improve the quality of the services offered by
decision-making support systems or recommender
systems. Such systems must often help a user choose
some alternative among a huge number of possibilities,
notably because of the combinatorial nature of the
alternatives. The goal of the system is thus to guide
its user in order to help her end up with her preferred
alternative. The efficiency of the system for this task
will be improved if it knows, at least partially, the user’s
preferences.
The notion of preferences has been studied in various
domains, notably in psychology, social choice theory,
micro-economics and decision theory. When studying
preferences of individuals that are supposed to be
rational, one can consider strict order relations:
the relation “is preferred to” is then supposed to be
irreflexive (M is never preferred to itself) and transitive
(if M is preferred to N, itself preferred to O, then M is
preferred to O).
Learning one’s preferences
Of course, one can only learn a user’s preferences if
some data about her is available. Therefore, we assume
that we are able to gather information about the user
during her interaction with the system. In particular,
we suppose that we can obtain pairwise comparisons
between alternatives (between menus in our example).
For instance, if at some point during the interaction
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with the system, the user modifies a menu that has been
suggested, we can record that she preferred the second
menu. It is these examples of the user’s preferences that
will be the basis of the learning process. The problem is
now to generalize these specific preferences, in order to
obtain a total order relation over the possible menus.
This induced relation can then be used to predict the
user’s preferences when the system suggests new menus.
As in any machine learning problem, the choice of
the type of model that one tries to learn is crucial.
We can try to learn ranking functions that associate
a numerical value to every alternative. The ADRIA
(Argumentation, Decision, Reasoning, Uncertainty and
Machine Learning) research group at IRIT studies the
induction of rules of the form: “If the main course is
fish, then white wine is preferred to red wine, whatever
the starter”. We try to learn an order relation that is
the transitive closure of pairwise comparisons implied
by such rules. Depending on the type of rules that are
authorized, one obtains classes of models of preferences
of various richness, that can be learnt efficiently or not.
In particular, the ADRIA group has characterized the
complexity of learning separable preferences (when
preferences over, for instance, the main course, the
wine, the starter and the dessert do not depend on one
another). We have also proposed algorithms to learn
lexicographic preferences - when some components of
the menu are more important than others. These results
have been obtained in collaboration with researchers
from the LAMSADE - University Paris-Dauphine and
from Mahasarakham University in Thailand.
Contact : [email protected]
Paul Sabatier University — Scientific Magazine — issue n°11
Reasoning and
decision
System security:
look for weaknesses
To find security flaws, programs now think like crackers.
>>> Yannick CHEVALIER,
UPS assistant professor
at the Institut de recherche en informatique
de Toulouse (IRIT, UPS/CNRS/INPT/UT1/UT2)
>>> A bike with two padlocks
awaits the reader in front of the IRIT
Consider two University of Toulouse students, Alice
and Bob, who share a bike. They don’t meet regularly,
but devised an ingenuous protocol to use the bike.
When Alice stops riding the bike, she puts her padlock
on it. When Bob plans to use the bike, he also puts
his padlock on it. This way, the next time Alice
sees the bike with two padlock on it, she can safely
remove hers, leaving Bob’s padlock on. He will then
later be able to use the bike. To sum up, Alice and
Bob have devised a set of rules such that, as long as
they adhere to it, they will be able to use the bike,
and the bike cannot be stolen. Computer scientists
use cryptographic algorithms instead of padlocks to
secure communications on the internet instead of a
bike, but the idea is the same. The security analysis of
cryptographic protocols consists in assessing where the
devised set of rules is sufficient to provide a claimed
guarantee. In plain text, is Alice and Bob’s confidence
that their protocol protects their bike well founded ?
While cryptographs are chiefly interested in a
padlock’s resistance (or rather on the security provided
by a cryptographic algorithm), the members of the
LILaC (Logic, Interaction, Language, and Calculus)
work on logical flaws, i.e. Flaws that do not rely
on lockpicking or on a shear, given the set of rules.
More specifically, they search algorithms able to
automatically find such flaws when they exist. For
example, if Charlie knows Alice and Bob’s protocol, he
can wait until there’s only Alice’s padlock on the bike,
put on another padlock looking like Bob’s, and wait
until Alice comes back and remove hers. Charlie will at
this point be able to ride away with the bike.
Logical analysis
They work on a logical model of the system under
scrutiny and of the goal properties. For example, a
logical modeling of a function f (e.g. a decryption
function) with one argument x would be a formula
stating “for any message x, either x cannot be computed
by the attacker or f(x) can be computed by the attacker”.
Similarly, we state that a message f(m) must remain
confidential by the logical formula “the attacker cannot
compute f(m)”. These expressions are clauses of firstorder logic. They express non-disjoint possible cases,
and their meaning is that for every ground value of
the variables at least one of the cases must be true.
When there are several such clauses there is a risk
that the cases are incompatible. For instance adding
the clause “the attacker can compute m” yields an
incompatible (logicians say unsatisfiable) set of clauses.
What’s interesting is that a set of clauses modelling
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a system together with its purported properties is
unsatisfiable when one of the properties does not hold.
Consequently, as logicians, our goal is to determine
whether a set of clauses modelling a system is
unsatisfiable.
Resolution
Though the problem is conceptually simple---it suffices
to try all possible instances of each variable and see
whether each clause is satisfied---it cannot be solved
by a machine in general because there is an infinite
number of possibilities for each variable. Alan
Robinson has however devised a principle he named
resolution that permits to speed up the examination of
all possible instances. It is based on the combination
of the cases occurring in the clauses. For instance,
if a clause states that “x cannot be computed by the
attacker or f(x) can be computed by the attacker”
while another states that “m can be computed by
the attacker”, resolution on the first case of the first
clause with the only case of the second clause yields a
clause stating “f(m) can be computed by the attacker”.
Using the resolution principle one adds new clauses
to a set of clauses. It is guaranteed that if the initial
set of clauses is unsatisfiable, one will end up adding
an unsatisfiable clause. But if the set of clauses is
satisfiable, the computation goes on indefinitely.
Unification
This principle is based on the detection of when two
clauses state a fact and its negation. One thus needs
to be able to compute when two facts have common
instances. This computation is called unification.
While in the basic case this problem is simple, the
security analysis of protocols depends upon additional
equalities constructions, expressing for instance
that the state of the bike with two padlocks is the
same regardless of whether Alice or Bob puts her/his
padlock first. The existence of such equalities makes
unification unsolvable by a machine. Given that both
detecting when two facts have common instances and
detecting when a set of clauses is unsatisfiable cannot
be solved in general by a machine, the work on security
in the LILaC team consists in finding classes of sets of
clauses and equality theories that are general enough
to specify the systems analyzed and specific enough
to be solvable by algorithms. For further information
on how this can applied to find a flaw on Google’s
implementation of SAML, we refer the reader to our
latest project website, http://www.avantssar.eu !
Contact : [email protected]
Reasoning and
decision
Artificial Intelligence
at work in negotiation
Which side to take in a trial? Which is the best medical decision to take?
When choices are difficult, artificial intelligence can provide valuable assistance in dissecting the foundations of an argument. It becomes a theoretical
tool for analyzing and formalizing the interactions between rational agents,
for example, in negotiation.
An opinion is justified by giving reasons that enforce
or explain it. These reasons, called arguments, can
take various forms, have different strengths, and
are more or less relevant with regard to the thesis.
Argumention is a process that consists of evaluating
and comparing arguments and counterarguments in
order to select the more acceptable ones.
For an autonomous agent, it is a major component
of reasoning, explanation of reasoning and decision
support, especially in the presence of contradictory
information.
>>> Argumentation in AI Group, ADRIA
and LILAC teams: Leila Amgoud (research
scientist, CNRS), Philippe Besnard (CNRS),
Claudette Cayrol (UPS professor),
Sylvie Doutre (associate professor at UT1),
Florence Dupin de St-Cyr (UPS associate
professor), Marie-Christine LagasquieSchiex (associate professor at UPS) in the
Toulouse Institute of Computer Science
Research (Institut de recherche en informatique de Toulouse, IRIT, UPS/CNRS/UT1/INP)
The chances of reaching a consensus
Argumention also plays an important role in multiagent interactions in general and in particular for
negotiating. Negotiation-based reasoning enables
agents to explain their choices with arguments.
In the light of a new argument, an agent may revise
its beliefs and preferences, increasing the chances
of reaching a consensus.
How to appreciate an argument? This is the central
issue on which the group “Argumentation in AI”
of IRIT is working.
The work of this group covers both the formal aspects
of argumention and the use of this formalism for
reasoning and decision problems. Regarding the
formal aspects, the group studies the interaction
between different types of arguments, the methods
of comparison and criteria for judging whether an
argument is acceptable, and the dynamics of a system
of argument, that is to say the change induced
by the inclusion of a new argument or the deletion
of an existing argument.
T1
B1
T2
B2
>>> An argumention dialogue: Tom (T1): “for going
downtown, my car is a good mode of transport”.
Bob (B1): “no, a car is a too dangerous mode of transport”.
Tom (T2): “no, my car is equipped with airbags”.
Bob (B2): “an airbag can explode!”.
Anne (A1): “anyway, there’s too much traffic to use the car”
Trials and medical decision
Formalisms are used to explain decisions, classify
objects, and to model negotiation between agents.
Although our research is usually very “upstream”,
it leads to many practical uses and affects many
different areas. Argumentation is used, for example,
to model and analyze legal arguments
(the transcript of a trial). There exist also numerous
applications in medicine; for example an argumentbased formalism has been used to produce a tool
managing the exchange of tissue between hospitals
in transplantation (European project ASPIC). Finally,
it is often used in trade negotiations on the web.
Contact : [email protected]
page 10
A1
Paul Sabatier University — Scientific Magazine — issue n°11
Reasoning and
decision
Thinking fast
without too much effort
Formal models of artificial intelligence require the development of algorithms that
automatically solve the problems they pose. An essential requirement is that they
do not consume too much computing time or too much memory.
The reconstruction of the shape of a 3D object from
a 2D line-drawing is an example of a problem that
can be modeled in terms of numerical, ordinal or
structural constraints together with preferences (for
flat surfaces and right angles, for example). Solving
these constraints allows a program to reconstruct
the object or to detect its physical impossibility.
>>> Martin Cooper and Olivier Gasquet,
UPS professors and researchers at IRIT (UMR UPS/
CNRS/INP/UT1/UT2)
The CSP (“Constraint Satisfaction Problem”) has
applications in many areas (such as in the aviation
or automobile industries), but if constraint problems
must be solved in real time, it is extremely difficult
to guarantee a quick response time. Techniques
known as “compilation” use off-line pre-processing
to solve part of the problem (the model of the system
to be diagnosed or the vehicle to be configured).
Members of our research team work with industrial
partners (Renault, Access Commerce) to integrate
preprocessed structures into configuration systems
for on-line sales.
Languages
In another line of research, the evolution of a
discrete system can be modeled as a “transition
system”, the transitions marking the change from
one system state to another. Examples include
executing a program, using a computer-security
protocol, driving a vehicle, or evolving information
(knowledge) within an artificial agent. “Can the
system get blocked? Does it contain unnecessary
states? Is it possible to reach a state satisfying a
(a) An impossible object; (b) a possible object.
page 11
given condition?”. At IRIT we design formal “modal”
languages in order to express such questions and to
provide an automatic answer
using calculations. Conversely, thanks to these modal
languages, it is possible to describe the properties
required of a system (this defines a modal logic).
Appropriate algorithms can then determine the
existence of a system, called a model, satisfying these
requirements and even build such a model.
Tractable problems
It is not only important to discover algorithms
and optimize them, but also to search for classes
of problems that can be solved by these algorithms.
Particular emphasis is placed on the identification of
so-called tractable classes of problems whose solution
time does not increase exponentially. A joint research
project with the University of Oxford has identified
several new tractable classes.
Our work has also given rise to the production
of free software: Toulbar2 (in collaboration with
INRA http://carlit.toulouse.inra.fr/cgi-bin/awki.
cgi/ToolBarIntro), which is a complete program for
solving valued constraint problems and LoTREC
(http://www.irit.fr/Lotrec), which is a development
platform for modal logic and model building.
Contacts : [email protected], [email protected]